For $U$ a balanced open subset of a Fréchet space $E$ and $F$ a dual-Banach space we introduce the topology ${\tau }_{\gamma }$ on the space $\mathscr{H}(U,F)$ of holomorphic functions from $U$ into $F$. This topology allows us to construct a predual for $(\mathscr{H}(U,F),{\tau }_{\delta })$ which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions....